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Pure point measures with sparse support and sparse Fourier-Bohr support
Citation
Baake, M and Strungaru, N and Terauds, V, Pure point measures with sparse support and sparse Fourier-Bohr support, Transactions of the London Mathematical Society, 7, (1) pp. 1-32. ISSN 2052-4986 (2020) [Refereed Article]
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Copyright Statement
Copyright 2020 The Authors. Licensed under Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) http://creativecommons.org/licenses/by-nc-nd/4.0/
Abstract
Fourier‐transformable Radon measures are called doubly sparse when both the measure and its transform are pure point measures with sparse support. Their structure is reasonably well understood in Euclidean space, based on the use of tempered distributions. Here, we extend the theory to second countable, locally compact Abelian groups, where we can employ general cut and project schemes and the structure of weighted model combs, along with the theory of almost periodic measures. In particular, for measures with Meyer set support, we characterise sparseness of the Fourier–Bohr spectrum via conditions of crystallographic type, and derive representations of the measures in terms of trigonometric polynomials. More generally, we analyse positive definite, doubly sparse measures in a natural cut and project setting, which results in a Poisson summation type formula.
Item Details
Item Type: | Refereed Article |
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Keywords: | aperiodicity, pure point measures, Fourier transform |
Research Division: | Mathematical Sciences |
Research Group: | Pure mathematics |
Research Field: | Lie groups, harmonic and Fourier analysis |
Objective Division: | Expanding Knowledge |
Objective Group: | Expanding knowledge |
Objective Field: | Expanding knowledge in the mathematical sciences |
UTAS Author: | Terauds, V (Dr Venta Terauds) |
ID Code: | 140823 |
Year Published: | 2020 |
Web of Science® Times Cited: | 1 |
Deposited By: | Mathematics |
Deposited On: | 2020-09-10 |
Last Modified: | 2020-10-09 |
Downloads: | 20 View Download Statistics |
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